1 / 21

Chapter 10 - Circles

Chapter 10 - Circles. Section 10.2 – Arcs and Chords. How Do You Measure a Circle or Parts of a Circle?. Area Circumference Arc length Arc measure. Unit Goal. Use properties of arcs of circles. A. is a central angle. P. B. Central Angles.

hasana
Download Presentation

Chapter 10 - Circles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 10 - Circles Section 10.2 – Arcs and Chords

  2. How Do You Measure a Circle or Parts of a Circle? • Area • Circumference • Arc length • Arc measure

  3. Unit Goal • Use properties of arcs of circles

  4. A is a central angle P B Central Angles • A central angle is an angle whose vertex is the center of the circle and whose sides intersect the circle.

  5. A P B Measuring Arcs • The measure of an arc is the same as the measure of its associated central angle.

  6. Major and Minor Arcs • A major arc is an arc whose measure is more than 180º. • A minor arc is an arc whose measure is less than 180º. • A semicircle is an arc that measures exactly 180º.

  7. Arc Naming Minor Arcs • Minor arcs are named by their endpoints.

  8. Arc Naming Major Arcs • Major arcs and semicircles are named by the two endpoints and a point on the arc.

  9. a. b. c. 70º Example • Find the measure of each arc:

  10. a. b. 90º c. 60º 40º Example • Find the measure of each arc:

  11. Find x and : Example

  12. Investigate on Circle C • Draw two distinct, congruent chords in circle C. • In a different color construct the central angles formed by the endpoints of your chords. • Find the measure of arc RJ and arc TK. • What do you notice?

  13. Congruent Chord Theorem In the same circle or congruent circles, two minor arcs are congruent iff their corresponding chords are congruent.

  14. ExampleFind the measure of arc BD.

  15. More with Circle C • Construct line through C that is perpendicular to • Name the point of intersection A • Construct line through C that is perpendicular to • Name the point of intersection E • Measure

  16. THEOREM In the same circle, or in congruent circles, two chords are congruent iff they are equidistant from the center.

  17. Investigate with Circle G • Construct a diameter • Construct a chord that is perpendicular to your diameter. Name the point of concurrency K. • Determine the measures of

  18. Diameter Bisector Theorem of Congruency

  19. Theorem If one chord is a perpendicular bisector of another chord, then the first chord is a diameter. This can be used to locate a circle’s center.

  20. Investigate on Circle E. • Draw any two chords that are not parallel to each other • Draw the perpendicular bisector of each chord. • The perpendicular bisectors should intersect at the circles center. • These are diameters.

  21. HW Assignment TB #2

More Related